What is the Perimeter of Quadrilateral Q? GMAT Data Sufficiency

Question: What is the perimeter of quadrilateral Q?

(1) Q is a rectangle.
(2) The area of Q is 25.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: E

Solution and Explanation:
Approach Solution 1:
Statement 1:
Insufficient

Statement 1:
If Q is square, P = 20
If Q is rectangle of 25x1, P=52
Insufficient

St1&2:
Same scenarios as statement 2
Insufficient

Approach Solution 2:
The key concept is to understand that the perimeter/area ratio decreases as the length and breadth of a rectangle converge: The minimum perimeter/area ratio is when the rectangle is a perfect square. Therefore, for a given area of a rectangle, its perimeter can be known only if the ratio of the length and breadth are known.

Statement (1) alone is insufficient, since we don't know the area nor its ratio;
Statement (2) alone is insufficient, since we don't know the type of quadrilateral, nor its perimeter, nor the ratio of the perimeter;
Both statements are insufficient also since we still don't know the ratio of the length and breadth.

Approach Solution 3:
Target question: What is the perimeter of quadrilateral Q?
If we recognize that each statement alone is not sufficient, we can jump straight to......

Statements 1 and 2 combined

There are several quadrilaterals that satisfy BOTH statements. Here are two:

Case a: Q is a rectangle with width 1 and length 25. In this case, the perimeter of quadrilateral Q is 1 + 1 + 25 + 25 = 52
Case b: Q is a rectangle with width 5 and length 5. In this case, the perimeter of quadrilateral Q is 5 + 5 + 5 + 5 = 20

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

“What is the perimeter of quadrilateral Q?”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Suggested GMAT Data Sufficiency Samples

• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X? GMAT Data Sufficiency
• 2x+3y GMAT Data Sufficiency
• The Selling Price of an Article is Equal to the Cost of the Article GMAT Data Sufficiency
• Equilateral triangle BDF Is Inscribed in Equilateral Triangle ACE GMAT Data Sufficiency
• What is the value of x if x^3 < x^2? GMAT Data Sufficiency
• If x ≠0, then what is the value of (|x|)x? GMAT Data Sufficiency
• What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair? GMAT Data Sufficiency
• Does The Equation y = (x – p)(x – q) Intercept The x-axis At GMAT Data Sufficiency
• S is a Set of n Consecutive Positive Integers. Is the Mean of the Set GMAT Data Sufficiency
• What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency
• If Vertices of a Triangle have Coordinates (-2,2) (3,2) GMAT Data Sufficiency
• If Set S Consists of Even Number of Integer, Is the Median GMAT Data Sufficiency
• What Is The Value Of N GMAT Data Sufficiency
• What is the value of x^2 + 1/x^2 ? GMAT Data Sufficiency
• Is the range of a combined set (S,T) bigger than the sum of the ranges of sets S and T? GMAT Data Sufficiency
• How many integers in a group of 5 consecutive positive integers are divisible by 4? GMAT Data Sufficiency
• Is the standard deviation of set S greater than the standard deviation of set T? GMAT Data Sufficiency
• Is a^7∗b^2∗c^3>0? (1) bc < 0 (2)ac > 0 GMAT Data Sufficiency
• If n is a non-negative integer, is 10^n+8 divisible by 18? GMAT Data Sufficiency
• Is the Range of Set S Greater than its Mean? GMAT Data Sufficiency
• Does the curve (x−a)^2+(y−b)^2=16 intersect the Y axis? GMAT Data Sufficiency
• If the average of four distinct positive integers is 60, how many integers of these four are less than 50? GMAT Data Sufficiency
• Is |x−1|<1? 1. (x−1)^2 ≤1 2. x^2−1>0 GMAT Data Sufficiency
• If the Vertices of a Triangle have Coordinates (x,1) (5,1) and (5,y) Where x<5 and y>1, What is the Area of the Triangle? GMAT Data Sufficiency
• Each Term of Set T is Multiple of 5. Is Standard Deviation of T Positive? GMAT Data Sufficiency
• Buster leaves the trailer at noon and walks towards the studio GMAT Data Sufficiency
• If x and y are positive integers and xy is divisible by prime number. Is p an even number? GMAT Data Sufficiency
• What is the Product of 6 Consecutive Numbers? GMAT Data Sufficiency
• If x is an integer is an x/12 integer? GMAT Data Sufficiency
• Is 7^7 / 7^x an integer? GMAT Data Sufficiency
• What is The Volume of the Right Circular Cylinder X ? GMAT Data Sufficiency
• If x>y^2>z^4, Which of The Following Statements Could Be True? GMAT Data Sufficiency
• A Clothing Manufacturer Makes Jackets That Are Wool or Cotton or a Combination of Wool and Cotton GMAT Data Sufficiency
• Is |x-1| < 1 ? 1. (x-1)^2 >1 2. x < 0 GMAT Data Sufficiency
• Is 2x - 3y < x^2 ? GMAT Data Sufficiency
• In Triangle PQR, if PQ = x, QR = x + 2, and PR = y GMAT Data Sufficiency
• In the Below Figure, O is The Centre of The Circle GMAT Data Sufficiency
• If p is the Perimeter of Rectangle Q, What is the Value of p? GMAT Data Sufficiency
• What is x? (1) x = 4y - 4 (2) xy = 8 GMAT Data Sufficiency
• Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0 GMAT Data Sufficiency
• What Is The Area Of Triangle ABC ? GMAT Data Sufficiency
• If n Is a Positive Integer And r Is The Remainder When n^2 - 1 is Divided By 8 GMAT Data Sufficiency
• If 0 < x < y, what is the value of (x+y)^2/(x−y)^2? GMAT Data Sufficiency
• If The Perimeter of Quadrilateral ABCD is 4, What Is Its Area? GMAT Data Sufficiency
• If Triangle ABC Is Isosceles, What Is The Length Of Side BC? GMAT Data Sufficiency
• Did Insurance Company K have More than $300 Million in Total Net Profits Last Year? GMAT Data Sufficiency
• Is x<5 ? (1)x^2 > 5 (2)x^2 + x < 5 GMAT Data Sufficiency
• Is x < y ? (1) 2x < 3y (2) xy > 0 GMAT Data Sufficiency
• Is c^(abcd) = 1? (1) |a|>|b|>|c|>|d| (2) c^d>3 GMAT Data Sufficiency
• Is n an even number GMAT Data Sufficiency